The folowing code produces 2 graphicses:
- LEFT ONE (denoted
slika1): camera view and an object (octahedron) - RIGHT ONE (denoted
slika2): rendered image of an object, given the coresponding view options
The center of view (denoted ViewC) (ABSOLUTE COORDINATES) is controled vith the first row of sliders.
The next three sliders control the displacement of camera from the center of view (denoted by ΔT).
In the code, the position of camera is denoted by T.
Clear["Global`*"];
\[Epsilon]=.000001;
(*
-TčjiKota je: {krak1, vrh, krak2}
-obr je obroba
-FaktZamikaKot: premakne napis v smeri navzven kota za ta faktor*VelNap
*)
PlotajKot3D[TčjiKota_,Rkota_,Bnot_,Bobr_,DebObr_,Npodkotov_,NapTex_,VelNap_,FaktZamikaKot_]:=(
(*
SetOptions[MaTeX,"Preamble"->{
"\\usepackage{color,bm}",
"\\definecolor{Bobr}{rgb}"<>ToString[Bobr[[;; 3]]]
}];
*)
VektKota1=TčjiKota[[1]]-TčjiKota[[2]];
VektKota2=TčjiKota[[3]]-TčjiKota[[2]];
kot=VectorAngle[VektKota1,VektKota2];
RMjikota=Table[RotationMatrix[\[Theta]kota,{VektKota1,VektKota2}],{\[Theta]kota,0,kot,kot/Npodkotov}];
LokKota=(TčjiKota[[2]]+Rkota # . Normalize[VektKota1])&/@RMjikota;
DaljiceLoka=Partition[LokKota,2,1];
TrikotnikiKota={
DaljiceLoka[[;;,1]],
Table[TčjiKota[[2]],Npodkotov],
DaljiceLoka[[;;,2]]
}\[Transpose];
Show[
Graphics3D[{RGBColor[Bnot],EdgeForm[],Polygon@#}]&/@TrikotnikiKota,
Graphics3D[{RGBColor[Bobr],Thickness->DebObr,Line@LokKota}](*,
Graphics3D[Text[
MaTeX["\\color{Bobr}"<>NapTex,
FontSize->VelNap],
TčjiKota[[2]]+(Rkota-FaktZamikaKot VelNap) Normalize[Normalize@VektKota1+Normalize@VektKota2]
]]*)
]
);
oktaeder=Graphics3D[{
RGBColor@{0,1,1,.5},EdgeForm[],
Polygon[{
{{1,0,0},{0,1,0},{0,0,1}},
{{-1,0,0},{0,1,0},{0,0,1}},
{{1,0,0},{0,-1,0},{0,0,1}},
{{-1,0,0},{0,-1,0},{0,0,1}},
{{1,0,0},{0,1,0},{0,0,-1}},
{{-1,0,0},{0,1,0},{0,0,-1}},
{{1,0,0},{0,-1,0},{0,0,-1}},
{{-1,0,0},{0,-1,0},{0,0,-1}}
}]
}];
res={resx,resy}=Round[{1920,1080}/2.7];
GEkrana[ViewC_,T_,d_,a_,\[CurlyPhi]_]:=(
\[CapitalDelta]T={x,y,z}=T-ViewC; (*relativni T, glede na ViewCenter*)
xy=Sqrt[x^2+y^2];(*POZOR!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
b=resy/resx a;
S=ViewC+(Norm[\[CapitalDelta]T]-d)Normalize@\[CapitalDelta]T;
\[CapitalDelta]x1=(b z x)/(2Norm[\[CapitalDelta]T]xy);
\[CapitalDelta]y1=(b z y)/(2Norm[\[CapitalDelta]T]xy);
\[CapitalDelta]z1=(b xy)/(2Norm[\[CapitalDelta]T]);
\[CapitalDelta]x2=(a y)/(2xy);
\[CapitalDelta]y2=(a x)/(2xy);
O1=S+{\[CapitalDelta]x1,\[CapitalDelta]y1,-\[CapitalDelta]z1}+{\[CapitalDelta]x2,-\[CapitalDelta]y2,0};
O2=S+{\[CapitalDelta]x1,\[CapitalDelta]y1,-\[CapitalDelta]z1}-{\[CapitalDelta]x2,-\[CapitalDelta]y2,0};
O3=S-{\[CapitalDelta]x1,\[CapitalDelta]y1,-\[CapitalDelta]z1}-{\[CapitalDelta]x2,-\[CapitalDelta]y2,0};
O4=S-{\[CapitalDelta]x1,\[CapitalDelta]y1,-\[CapitalDelta]z1}+{\[CapitalDelta]x2,-\[CapitalDelta]y2,0};
rot=RotationMatrix[\[CurlyPhi],\[CapitalDelta]T];
O1=S+rot . (O1-S);
O2=S+rot . (O2-S);
O3=S+rot . (O3-S);
O4=S+rot . (O4-S);
Oji={O1,O2,O3,O4};
rViewSfere=Max[Norm[# - ViewC] & /@ {T, O1}];
ViewSfera=Sphere[ViewC, rViewSfere];
(*zdej pa še dobimo žarke na drug stran ViewSfere*)
TO1=O1-T;
lžarkov=2 rViewSfere Cos@VectorAngle[-\[CapitalDelta]T,TO1];
žarki={T,T+lžarkov Normalize[#-T]}&/@Oji;
PiramidaŽarkov=Polygon[{
žarki[[;;,2]],
RotateRight@žarki[[;;,2]],
žarki[[;;,1]]
}\[Transpose]];
(*
Graphics3D[Text["1",O1]],
Graphics3D[Text["2",O2]],
Graphics3D[Text["3",O3]],
Graphics3D[Text["4",O4]],
*)
slika1=Show[
Graphics3D[Point@ViewC],
Graphics3D[{Green,Point[T]}],
Graphics3D[Point[S]],
Graphics3D[{White,Line[{T,ViewC}]}],
Graphics3D[{Yellow,Line@žarki}],
Graphics3D[{RGBColor@{1,1,0,.5},EdgeForm[{RGBColor@{1,1,0,.9},[email protected]}],Polygon@Oji}],
Graphics3D[{[email protected],ViewSfera}],
Graphics3D[{RGBColor@{1,1,0,.06},EdgeForm[],PiramidaŽarkov}],
Graphics3D[{
RGBColor[{1,0,0}],Arrowheads[.008],
ViewVIzh=Mean@{O3,O4}; RViewV=.8; ViewV=RViewV Normalize[O4-O1];
Arrow[Tube[{{0,0,0},ViewV}+Threaded[ViewVIzh,2], .012]]
}],
PlotajKot3D[
{\[CapitalDelta]T,{0,0,0},-\[CapitalDelta]T+\[Epsilon] ViewV}+Threaded[ViewVIzh,2],
RViewV,RGBColor@{1,0,0,.1},RGBColor@{0,0,0,0},.01,30,"",15,0],
oktaeder,
Boxed->False,Background->Black,Lighting->"Neutral",
ViewPoint->{0, -2, .5},ViewVertical->{0, 0, 1},
SphericalRegion->ViewSfera,
ImageSize->{resy,resy}
];
slika2=Show[
oktaeder,
Boxed->False,Background->Black,Lighting->"Neutral",
ViewPoint->T, ViewVector -> {Scaled@T, ViewC},
ViewAngle->ArcTan[b/(2 d)],ViewVertical->ViewV,
ImageSize->res
];
{slika1,slika2}
);
Manipulate[
GEkrana[ViewC,ViewC+r{Cos[\[Beta]]Cos[\[Alpha]],Cos[\[Beta]]Sin[\[Alpha]],Sin[\[Beta]]},d,2 d Tan[ViewA],\[CurlyPhi]],
Style["ViewCenter in absolute coordinates",15,Bold],
{{ViewC,{0,0,0}},{-1,-1,-1},{1,1,1}},
Delimiter,
Style["\[CapitalDelta]Viewpoint",15,Bold],
{{\[Alpha],.6},0,2\[Pi]},
{{\[Beta],.2},-\[Pi]/2+\[Epsilon],\[Pi]/2-\[Epsilon]},
{{r,5},\[Epsilon],10},
Delimiter,
Style["ViewAngle",15,Bold],
{{d,2},\[Epsilon],10},
{{ViewA,15°},\[Epsilon],\[Pi]/2-\[Epsilon]},
Delimiter,
Style["ViewVertical je poljuben
\[RightVector] iz rdeče polravnine",15,Bold],
{{\[CurlyPhi],0},0,2\[Pi]},
ControlPlacement->Left
]
For slika2, I first tried the option ViewCenter -> Scaled@ViewC. The result was wrong. Then I read this post: Am I missing the point of ViewCenter?. The answer in it advised ViewVector -> {Scaled@T, ViewC}. In my case this gives more accurate result, but it is still wrong.
For example: if I leave the ViewC at the oreign {0,0,0} and delete ViewVector -> {Scaled@T, ViewC} from the code, using the same parameters, I get different result, without ViewVector -> {Scaled@T, ViewC}, then with it. This is shown on the nex image.
Also you see on the left image, that the bottom vertex should be on the image. But if you look on the right image, the bottom vertex is not on the image.
How to fix it?
